let R be Relation; :: thesis: for S being complex-valued Relation st R c= S holds
R is complex-valued
let S be complex-valued Relation; :: thesis: ( R c= S implies R is complex-valued )
assume R c= S ; :: thesis: R is complex-valued
then A1: rng R c= rng S by RELAT_1:11;
rng S c= COMPLEX by Def1;
hence rng R c= COMPLEX by A1, XBOOLE_1:1; :: according to VALUED_0:def 1 :: thesis: verum